I have no made this style either, but according to the BJCP description that JZ and Gordon Strong helped a revise:
Flavor: Strong, intense, complex, multi-layered malt flavors ranging from bready and biscuity through nutty, deep toast, dark caramel, toffee, and/or molasses. Moderate to high malty sweetness on the palate, although the finish may be moderately sweet to moderately dry (depending on aging). Some oxidative or vinous flavors may be present, and often complex alcohol flavors should be evident. Alcohol flavors shouldn’t be harsh, hot or solventy. Moderate to fairly high fruitiness, often with a dried-fruit character. Hop bitterness may range from just enough for balance to a firm presence; balance therefore ranges from malty to somewhat bitter. Low to moderately high hop flavor (usually UK varieties). Low to no diacetyl.
Mouthfeel: Full-bodied and chewy, with a velvety, luscious texture (although the body may decline with long conditioning). A smooth warmth from aged alcohol should be present, and should not be hot or harsh. Carbonation may be low to moderate, depending on age and conditioning.
To me that means something in the 75-80% attenuation range.
I don't know what OG you're shooting for, but let's say you want to hit 1.110. It sounds like you want it to finish a bit dry so maybe you're thinking about 1.020 or so. That's an aa of about 81%, which is pretty good for any yeast, and most likely isn't going to dry this beer out very much. (I think we've both had beers that finished at 1.020 or higher and can attest to the remaining residual sweetness).
Barleywine's are supposed to be big, thick and chewy. If you want to dry it out maybe toss in some sucrose and maybe some treacle.
Of the 2 Wyeast strains you presented, I'd go with the Thames. If you really want it dry, I'm guessing that Nottingham will get the TG lower than the Thames.